In a previous lesson, students solved systems of linear equations by graphing. Here, they transition to solving systems algebraically—by substitution—and to reasoning about systems without a context.
The lesson activates and builds on what students have learned in grade 8 about solving by substitution. Students see that a system can be solved by replacing a variable with a number or with an expression, and that various substitutions can be done to solve the same system. They also begin to build an awareness of the kinds of systems that are conducive to being solved by substitution.
Students practice looking for and making use of structure as they identify the variables or expressions to substitute and ways to perform substitutions efficiently (MP7).
Lesson overview
 13.1 Warmup: Math Talk: Is It a Match? (5 minutes)
 13.2 Activity: Four Systems (15 minutes)

13.3 Activity: What about Now? (10 minutes)
 Includes "Are you Ready for More?" extension problem
 Lesson Synthesis
 13.4 Cooldown: A System to Solve (5 minutes)
Learning goals:
 Recognize that a system can be efficiently solved by substitution if one variable is already isolated or can be easily isolated.
 Recognize that there are multiple ways to perform substitution to solve a system of equations.
 Solve systems of linear equations by substituting a variable with a number or an expression, and check solutions by substituting them back into the equations.
Learning goals (student facing):
 Let’s use substitution to solve systems of linear equations.
Learning targets (student facing):
 I can solve systems of equations by substituting a variable or an expression.
 I know more than one way to perform substitution and can decide which way or what to substitute based on how the given equations are written.
Required preparation:
 Access to graphing technology available for students.
Glossary:
 substitution  Substitution is replacing a variable with an expression it is equal to.
 Access the complete Algebra 1 Course glossary.
Standards:
 This lesson builds on the standards: CCSS.8.EE.B.6MS.8.EE.6CCSS.HSAREI.D.10MS.AREI.10MO.8.EEI.B.6bMO.A1.REI.C.6
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